On the Statistical Multiplexing Gainof Virtual Base Stations Pools

Lewis (Jingchu) LIU, Sheng ZHOU, Jie GONG, Zhisheng Niu,Tsinghua University, Beijing, China

Shugong XUIntel Labs, Beijing, China

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 2

Contents

• Background and motivation• Session-level model for VBS pools• Blocking probabilities• Statistical multiplexing gain• Numerical results• Summary

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 3

Background and Motivation

• Challenges to cellular networks• Interference in HetNets and Small Cell settings• High operational costs and low resource utilization

• C-RAN is emerging as the new RAN architecture[CRAN][NGMN][WNC]

• Baseline structure: distributed RRU, centralized BBU• Tech. advantages: simplified BS cooperation• Economic advantage: reduced site expenditure (rent, electricity, site visit)

• GPP based BS virtualization and pooling[CIQ][VBS][BigStation]

• Statistical multiplexing gain by baseband consolidation• Flexible in adding new functionalities and provisioning computational resources

for , more complex baseband processing• Fronthaul challenge in C-RAN

• Bandwidth: 1.25Gbps / 20Mhz LTE AxC [CPRI] , each site has multiple A and C• Delay: 4ms deadline of HARQ in LTE• Thus, centralization cost of C-RAN is huge (In sheer contrast with Internet Cloud)

BS = Base StationGPP = General Purpose PlatformAxC = Antenna x Carrier

Need to balance the gains and costs of centralization!

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 4

Background and Motivation

• Why model dynamics of VBS pools?• Tell the pooling gain under different pool size, traffic load, etc.• Can be incorporated with cost models to evaluate tradeoffs

• Previous models [Gomez’13]

• Dynamic resource management (per task) algorithm is not realistic; semi-dynamic (per session) resource management is more realistic

• Not consider the constraint of radio resource, which is equally important in VBS pool to computational resources

• Our proposal• Captures the session-level dynamics in VBS pools• Assumes session-by-session resource scheduling• Reflects both radio and computational resources constraints

To study the tradeoffs, first we should have a model…

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 5

Session-Level Model for VBS Pools- Model basics

• Pool parameters• Consolidating VBSs in the pool• Each VBS has units of radio resources (r-server) in its serving cell• All VBSs share a total of units of computational resources (c-server)

• Traffic arrival and service discipline• Independent Poisson session arrival to each VBS, rate • Session serviced with exponential service time with mean

• Resource scheduling by blocking and clear• Each session occupy 1x r-server and 1x c-server simultaneously• Arriving session is blocked if either type of serve is used up.

Radio – computation double constraint

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 6

Session-Level Model for VBS Pools- Equivalence to Markov chain

• Multi-dimensional Markov process• Arrival and service is memory-less (a.k.a Markovian)• Pool state vector (# of sessions) is a multi-dimensional Markov chain

• Possible states due to double constraints

• Birth-and-death state transitionOnly neighboring states has

non-zero transitions rate

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 7

Session-Level Model for VBS Pools- Equivalence to Markov chain, cont‘d

• 2-Dimensional Example (M = 2, K = 3, N = 4)• Intuition: possible states lies in the remaining part of a M-dimensional

cube after its N-corner is cut off.

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 8

Session-Level Model for VBS Pools- Model solution

• Stationary distribution (see paper for detail)• Local balance equation holds (due to reversibility)

• Product-form stationary distribution !

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn

Blocking Probabilities- Straight-forward evaluation

• Significance of blocking probabilities• QoS is reflected ONLY by blocking probabilities in our model

• Blocking events break up• Computational blocking Bc: Due to in-sufficient c-servers • Radio blocking Br: Due to in-sufficient r-servers, but not c-servers

• Straight-forward calculation

9Exhaustive summation, exponential complexity, intractable!

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 10

Blocking Probabilities- Recursive evaluation

• First, define two auxiliary functions…

• which we can use to express blocking probabilities

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 11

Blocking Probabilities- Recursive evaluation

• These functions can be evaluated recursively

• Now the complexity is quadratic to the pool size!

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 12

Statistical Multiplexing Gain- Large Pool Limit

• Asymptotic resource utilization ratio in large pools

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 13

Numerical Results- Knee Point Effect

Knee point effect, knee point is the minimum allowable amount of computational resources.

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 14

Numerical Results- Decreasing Marginal Pooling Gain

• Decreasing marginal pooling gain• Pooling gain increases fast with medium size (M=64)• But marginal gain soon diminishes (M=100 close to M=64)• Preliminary Estimation [CLT + Chernoff Bound]

• Large Pool Limt: , Knee Point:

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 15

Numerical Results- Influence of traffic and QoS

Larger traffic pushes curve to the right;Stricter QoS pushes curve down

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 16

Future Work

• Pooling gain approximation (Closed-form, other traffic)• Verification of Markov Assumption (Exp. Service Time)• Dynamics in other level (Baseband Task Processing)

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 17

Conclusion

• Multi-dimensional Markov model• Captures the session-level dynamics in VBS pool• Reflects the interaction btw. radio and computational resources

• Model Solutions• Exist product-form stationary distribution• Recursive method to evaluate QoS (Pb)• Simple large pool limit

• Numerical Results and Discussion• “Knee” point effect• Decreasing marginal pooling gain• Lighter traffic or stricter QoS = Larger pooling gain

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 18

Thanks

• Thanks!• Questions?

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 19

Reference

[CRAN] China Mobile, “C-RAN: The road towards green RAN,” 2011.[NGMN] NGMN Alliance, “Suggestions on potential solutions to C-RAN,” 2013.[WNC] Y. Lin, L. Shao, Z. Zhu, Q. Wang, and R. K. Sabhikhi, “Wireless network cloud: Architecture and system requirements,” IBM Journal of Research and Development, vol. 54, no. 1, pp. 4–1, 2010.[CIQ] S. Bhaumik, S. P. Chandrabose, M. K. Jataprolu, G. Kumar, A. Muralidhar, P. Polakos, V. Srinivasan, and T. Woo, “CloudIQ: a framework for processing base stations in a data center,” in Proceedings of the 18th annual international conference on Mobile computing and networking. Istanbul, Turkey: ACM, 2012, pp. 125–136, 2348561.[VBS] Z. Zhu, P. Gupta, Q. Wang, S. Kalyanaraman, Y. Lin, H. Franke, and S. Sarangi, “Virtual base station pool: towards a wireless network cloud for radio access networks,” in Proceedings of the 8th ACM International Conference on Computing Frontiers. ACM, 2011, p. 34.[BigStation] Q. Yang, X. Li, H. Yao, J. Fang, K. Tan, W. Hu, J. Zhang, and Y. Zhang, “BigStation: enabling scalable real-time signal processing in large mu-mimo systems,” in Proceedings of the ACM SIGCOMM 2013 conference. Hong Kong, China: ACM, 2013, pp. 399–410, 2486016.[CPRI] CPRI Cooperation, “CPRI specification v6.0; interface specification,” 2013.[Gomez’13] I. Gomez-Miguelez, V. Marojevic, and A. Gelonch, “Deployment and management of sdr cloud computing resources: problem definition and fundamental limits,” EURASIP Journal on Wireless Communications and Networking, vol. 2013, no. 1, pp. 1–11, 2013.

Lewis LIU, liu-jc12@mails.tsinghua.edu.cn 20